Ok lets hypothetically explore the two. (but there are in fact 3 scenarios to consider.)
Hypothetical person 1 is a straight guy who is a pervert and so he pretends he is transgender so he can go into the ladies restrooms.
Now think about this a bit more in dept as to do this he will need to obtain women's clothing etc. I would be surprised if such a man would prepare him self at home as if he does, there is a good chance a neighbour will see him walk out his front door and start his car and drive away. He has to change some place else. His next issue is upon going in, what ever he does he will be seen by other women and as the chances of him seeing what he desires as soon as he walks in is very small, women will quickly challenge this person who they observe has hairy legs and arms and big hands and fingers and incorrect fitted shoes. They would because in order to be in place at that rignt moment he would need to loiter in the restroom for a long time to obtain his desired opportunity to perve.
In fact if you are sincere such a man would do better dressing up as a cleaner which would justify him being in the restrooms. My understanding is a couple of men have given this a go and failed miserably.
Meanwhile across the road our second hypothetical person who is a true transgender person would enter the restrooms there and inside she enters a cubicle, do what was required, flushes and wash her hands then leaves. In and out in a matter of minutes not drawing attention to her self.
Anyone who did see her would have just a matter of seconds to draw a conclusion. That is how long it takes to enter the restrooms and go into a cubicle. Most children are so wrapped up in their own world they would not realise unless a nutter was to make a fuss. Remember this person is no danger to children, its your sicko perve who is.
Now lets follow the idea promoted by some that says out trans person knows that her going into the ladies make some young (and old) women uncomfortable. To avoid that she looks at the alternative.
She says I will go to the men's restrooms.
Young friends John and Chris are standing at the urinal with the family jewels in hand releasing their load and look up as our hypothetical transgender women walk in the door?
Do you not think these boys or even adult men would distressed at what appears to be a women walking in on them?